The magnetic field (B-field) of the starless dark cloud L1544 has been studied using near-infrared (NIR) background starlight polarimetry (BSP) and archival data in order to characterize the properties of the plane-of-sky B-field. NIR linear polarization measurements of over 1700 stars were obtained in the H band and 201 of these were also measured in the K band. The NIR BSP properties are correlated with reddening, as traced using the Rayleigh-Jeans color excess (H-M) method, and with thermal dust emission from the L1544 cloud and envelope seen in Herschel maps. The NIR polarization position angles change at the location of the cloud and exhibit their lowest dispersion there, offering strong evidence that NIR polarization traces the plane-of-sky B-field of L1544. In this paper, the uniformity of the plane-of-sky B-field in the envelope region of L1544 is quantitatively assessed. This allows evaluation of the approach of assuming uniform field geometry when measuring relative mass-to-flux ratios in the cloud envelope and core based on averaging of the radio Zeeman observations in the envelope, as done by Crutcher et al. (2009ApJ...692..844C). In L1544, the NIR BSP shows the envelope B-field to be significantly non-uniform and likely not suitable for averaging Zeeman properties without treating intrinsic variations. Deeper analyses of the NIR BSP and related data sets, including estimates of the B-field strength and testing how it varies with position and gas density, are the subjects of later papers in this series.